Lino O. Santos

Nonlinear model predictive control of fed-batch cultures of micro-organisms exhibiting overflow metabolism: Assessment and robustness

Overflow metabolism characterizes cells strains that are likely to produce metabolites as, for instance, ethanol for yeasts or acetate for bacteria, resulting from an excess of substrate feeding and inhibiting the cell respiratory capacity. The critical substrate level separating the two different metabolic pathways is generally not well defined. This occurs for instance in Escherichia coli cultures with aerobic acetate formation. This work addresses the control of a lab-scale fed-batch culture of E. coli with a nonlinear model predictive controller (NMPC) to determine the optimal feed flow rate of substrate. The objective function is formulated in terms of the kinetics of the main metabolic pathways, and aims at maximizing glucose oxidation, while minimizing glucose fermentation. As bioprocess models are usually uncertain, a robust formulation of the NMPC scheme is proposed using a min–max optimization problem. The potentials of this approach are demonstrated in simulation using a Monte-Carlo analysis.

Reliable and Efficient Optimization Strategies for Nonlinear Model Predictive Control

Abstract Previous experience with predictive control algorithms has shown that the way the optimization problems are formulated and solved has a big impact in the success of the control strategy. Here a multiple shooting formulation is proposed, where a process model is integrated separately inside each sampling interval, and the corresponding equality constraints are added directly to the optimization problem. It is shown that the resulting formulation provides a more reliable framework for the solution of predictive control problems, both in the linear and nonlinear cases. This strategy is compared with the original nonlinear Newton-type (state space) algorithm, on a number of process models with challenging features, including the reactor model from the Tennessee Eastman problem.

A tool to analyze robust stability for model predictive controllers

Abstract A strategy based on Nonlinear Programming (NLP) sensitivity is developed to establish stability bounds on the plant/model mismatch for a class of optimization-based Model Predictive Control (MPC) algorithms. By extending well-known nominal stability properties for these controllers, we derive a sufficient condition for robust stability of these controllers. This condition can also be used to assess the extent of model mismatch that can be tolerated to guarantee robust stability. In this derivation we deal with MPC controllers with final time constraints or infinite time horizons. Also for this initial study we concentrate only on discrete time systems and unconstrained state feedback control laws with all of the states measured. To illustrate this approach we give two examples: a linear first-order dynamic system and a nonlinear SISO system involving a first order reaction. ©

Modeling the effect of mixing in biodiesel production

The transesterification reaction models available in the literature are valid only for one particular mixing condition. In this work, a modeling strategy is presented in order to predict the effect of mixing conditions in the transesterification process. The proposed methodology was applied to independent sets of experimental data available in the literature that show the dependency of the transesterification reaction on the frequency of rotation of the stirrer. The accuracy of the developed models corroborates the validity of the proposed modeling approach.

Optimal sizing, scheduling and shift policy of the grinding section of a ceramic tile plant

This paper addresses the optimal design of the grinding section of a ceramic tile plant operating in a cyclic mode with the units (mills) following a batch sequence. The optimal design problem of this single product plant is formulated with a fixed time horizon of one week, corresponding to one cycle of production, and using a discrete-time resource task network (RTN) process representation. The size of the individual units is restricted to discrete values, and the plant operates with a set of limited resources (workforce and equipment). The goal is to determine the optimal number and size of the mills to install in the grinding section, the corresponding production schedule, and shift policy. This problem involves labor/semi-labor intensive (LI/SLI) units with a depreciation cost of the same order as that of the operation cost. The optimal design of the grinding section comprises the trade-off between these two costs. The resulting optimization formulation is of the form of a mixed integer linear programming (MILP) problem, solved using a branch and bound solver (CPLEX 9.0.2). The optimal solution is analyzed for various ceramic tile productions and different shift policies. Scope and Purpose: This paper addresses an optimal design case study of the grinding section of a ceramic tile plant with respect to the net capacity to install, the operation scheduling and the shift policy to implement. A mathematical programming model is formulated based on the resource task network (RTN) framework representation. The problem is solved using a branch and bound algorithm. The main goal of this work is to apply optimal design/scheduling general tools to real problems commonly found in the ceramic industry sector, a particular case of labor intensive plants. The application of these methodologies to this case study demonstrates as well the importance of adopting suitable optimization strategies for plant design in order to improve the economical performance of the production lines.

A Nonlinear Model Predictive Control Framework as Free Software: Outlook and Progress Report

Model predictive control (MPC) has been a field with considerable research efforts and significant improvements in the algorithms. This has led to a fairly large number of successful industrial applications. However, many small and medium enterprises have not embraced MPC, even though their processes may potentially benefit from this control technology. We tackle one aspect of this issue with the development of a nonlinear model predictive control package NEWCON that will be released as free software. The work details the conceptual design, the control problem formulation and the implementation aspects of the code. A possible application is illustrated with an example of the level and reactor temperature control of a simulated CSTR. Finally, the article outlines future development directions of the NEWCON package.

Mechanism of supplemental activator and reducing agent atom transfer radical polymerization mediated by inorganic sulfites: experimental measurements and kinetic simulations

The mechanism of atom transfer radical polymerization (ATRP) mediated by sodium dithionite (Na2S2O4), with CuIIBr2/Me6TREN as catalyst (Me6TREN: tris[2-(dimethylamino)ethyl]amine)) in ethanol/water mixtures, was investigated experimentally and by kinetic simulations. A kinetic model was proposed and the rate coefficients of the relevant reactions were measured. The kinetic model was validated by the agreement between experimental and simulated results. The results indicated that the polymerization followed the SARA ATRP mechanism, with a SO2•- radical anion derived from Na2S2O4, acting as both supplemental activator (SA) of alkyl halides and reducing agent (RA) for CuII/L to regenerate the main activator CuI/L. This is similar to the reversible-deactivation radical polymerization (RDRP) procedure conducted in the presence of Cu0. The electron transfer from SO2•-, to either CuIIBr2/Me6TREN or R-Br initiator, appears to follow an outer sphere electron transfer (OSET) process. The developed kinetic model was used to study the influence of targeted degree of polymerization, concentration of CuIIBr2/Me6TREN and solubility of Na2S2O4 on the level of polymerization control. The presence of small amounts of water in the polymerization mixtures slightly increased the reactivity of the CuI/L complex, but markedly increased the reactivity of sulfites.

Hybridoma cell culture optimization using nonlinear model predictive control

Abstract This work addresses the application of control systems to the optimization of a monoclonal antibodies (MAb) production chain. The attention is focused on the maximization of hybridoma fed-batch culture productivity. The proposed model presents kinetics showing strong nonlinearities through min-max functions expressing overflow metabolism. A nonlinear model predictive control (NMPC) algorithm, choosing the best trajectory over a moving finite horizon among different sequences of inputs, is suggested in order to optimize productivity. Sensitivities of selected objective functions are considered in a minimax robust version of the NMPC in order to choose the best configuration with respect to practical operating conditions.

Nonlinear model predictive control of fed-batch cultures of micro-organisms exhibiting overflow metabolism

Overflow metabolism characterizes cells strains that are likely to produce inhibiting metabolites resulting from an excess of substrate feeding and a saturated respiratory capacity. The critical substrate level separating the two different metabolic pathways is generally not well defined. This occurs for instance in Escherichia coli cultures with aerobic acetate formation. This paper considers the control problem of a lab-scale E. coli biomass production. A preliminary study is presented to access the application of a multivariable nonlinear model predictive control approach to maximize the biomass production. This strategy is tested by simulation and its performance to control the bioreactor system is evaluated with various objective cost functions, and in the presence of noise and dead-time on the acetate concentration measurement.

A Tool to Analyze Robust Stability for Constrained MPC

Abstract A sufficient condition for robust stability of nonlinear constrained Model Predictive Control (MPC) with respect to plant/ model mismatch is derived. This work is an extension of a previous study On the unconstrained nonlinear MPC problem, and is based on Nonlinear Programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measmed. A strategy to estimate bounds on the plant/model mismatch is proposed, that can be used off-line as a tool to assess the extent of model mismatch that can he tolerated to guarantee robust stability.